How to present and use statistics
Chris Robertson
David Young
Department of Statistics and Modelling Science,
University of Strathclyde
Health Protection Scotland
Royal Hospital for Sick Children,
Yorkhill NHS Trust
YORKHILL HOSPITAL
Outline
o Introduction
o What is statistics
o Hypotheses
o Statistics in Medical Research
o Study Design
Principles
Main Types
o Data and Presentation
o Types of data
o Graphical Methods
o Tables
2
Introduction
o what is statistics and why do we need it?
o statistics is the science of collecting, analysing, presenting
and interpreting data
o it enables the objective evaluation of research questions of
interest
o it provides the means to weigh up how much evidence the
collected data provide for and against the research
hypothesis of interest
3
Examples of Research Hypotheses
o The main aim of this prospective cross-over study was to
introduce one additional cleaner into a surgical ward from
Monday to Friday and measure the effect on the clinical
environment. After 6 months the cleaner was switched to
another matched surgical ward so that each ward acted as a
control for the other.
Measuring the effect of enhanced cleaning in a UK hospital: a
prospective cross-over study
Stephanie J Dancer, Liza F White, Jim Lamb, E Kirsty Girvan and Chris Robertson
BMC Medicine 2009, 7:28 doi:10.1186/1741-7015-7-28
4
Examples of Research Hypotheses
o The aim of this review was to assess whether the reported
rate of infection (i.e. incidence) or reported rate of death
among patients with CDAD for any particular month within
an acute hospital, or any particular acute hospital, differs
from other months, other acute hospitals, or the national
average in Scotland.
Report on Review of Clostridium difficile Associated Disease Cases and Mortality in all Acute Hospitals in
Scotland from December 2007 ─ May 2008
Health Protection Scotland, 2008
http://www.documents.hps.scot.nhs.uk/hai/sshaip/publications/cdad/cdad-review-2008-07.pdf
5
Examples of Research Hypotheses
o The aims of the survey were: To provide the HAITF with
baseline information on the total prevalence of HAI in
Scottish hospitals and its burden in terms of health service
utilisation and costs. This information would be available to
guide priority setting in the development of strategy and
policy.
NHS Scotland National HAI Prevalence Survey. Volume 1 of 2. Final Report
Health Protection Scotland, 2007
http://www.hps.scot.nhs.uk/haiic/publicationsdetail.aspx?id=34832
6
Statistics and Medical Research
o statistics plays an increasingly important role in medical
research
o it is not possible, for example, to have a new drug treatment
approved for use without solid, statistical evidence to
support claims of efficacy and safety
o over the last few decades, many new statistical methods
have been developed which have particular relevance for
medical researchers
o these methods can be applied routinely using statistical
software packages
o easy to use but difficult to use correctly
7
Importance of Statistics
Medical researchers should understand some basic statistical
concepts to ensure …
o appropriate study design in terms of the number of
participants
o application of the correct method of statistical analysis
when using software
o accurate and honest reporting of data gathered from
research studies
o adequate understanding of claims made by other
researchers when reviewing medical literature
8
The study design
o
o
o
o
o
o
o
o
one of the main areas of research in which statisticians can
work with other researchers to design the optimal studies
describe the broad class of study design using standard
terminology e.g. case study, cross-sectional study, cohort
study, case-control study, clinical trial
study intervention should be explained
objectives should be clearly stated
state the outcome measure of interest
distinction between pre- and post-study hypotheses
inclusion and exclusion criteria of patient population
source of study subjects
9
Study design (cont.)
o
o
o
o
choice of control group – concurrent or historical
blinding – ideal is to use double blinding if possible and
justification for not should be given
randomisation with details of any factors by which the
stratification had been carried out
power and sample size – details of how the sample size was
chosen including the power and minimum clinically
important effect
10
Study Design
1.
2.
3.
4.
5.
6.
research idea
broad research questions
primary research question
primary hypothesis
secondary research questions
secondary hypotheses
11
Randomised Controlled Trials
Interventional
l
l
l
l
l
population
sample
inclusion/exclusion criteria
randomisation – treatments A or B
comparison of outcomes between A and B using
statistical tests
12
Cohort Study (longitudinal/prospective)
Observational
l
l
l
l
subjects without the disease (cohort)
either exposed (e.g. smoker) or not exposed (e.g. nonsmoker)
proportion of each group will develop the disease (e.g.
lung cancer)
compare proportions in each group using statistical tests
13
Case/Control (retrospective)
Observational
l
l
l
people with and without the disease (i.e. cases and
controls)
observe the exposure factor (e.g. past smoking habits)
compare proportions in cases and control who were
exposed to the variable of interest (e.g. smoking)
14
Cross-sectional (prevalence)
o usually carried out using a survey (questionnaire)
o used to quantify specified characteristics of a defined group
of people
o number of people with attribute at a specified point in time
reported as a proportion of the population of interest
(prevalence)
15
Examples
o a survey of HPV Prevalence among school children in
Scotland
o cross sectional survey
o evaluation of the effect of an additional cleaner on the total
coliform count on hand touch sites in a ward
o randomised trial
o exposure to unfiltered water increases the risk of
campylobacter infection
o case control study
o association between H1N1v Influenza vaccination and the
risk of hospitalisation for flu like symptoms
o cohort study
16
Presentation of Statistical Data
l
l
l
l
Keep it clear and simple
Methods used depend upon the types of
data recorded
do not include graphs of relatively
unimportant data
where the number of observations is
small, plots are not useful (e.g. mean
values with error bars)
17
Types of Data
categorical data
•
•
nominal – the data can be classified into a number of
specific categories with no particular ordering e.g. blood
type, HAI (Yes/No), Test Outcome
(Positive/Negative/Ambiguous)
ordinal – the data can be classified into a number of
specific categories which can be placed in some order of
importance e.g. pain scores (mild, moderate, severe or
unbearable), deprivation category score within Glasgow
(ranges 1–7 from affluent to poor classified by postcodes)
18
Types of Data
numerical data
•
•
discrete – data are recorded as a whole number and usually
only take specific values e.g. number of cigarettes smoked
in a day, number of children, number of admissions
continuous – data are recorded to the precision of the
measuring instrument and usually take any value within a
certain range e.g. height, weight, blood pressure,
19
Numerical presentation of data
o
o
o
o
o
appropriate numerical summaries should give an overall
unambiguous impression of the data
means should be quoted to at most one extra decimal place
relative to the precision with which the original
measurements were recorded
standard deviations and standard errors may be quoted with
two additional decimal places
medians and IQR handled as for means
avoid use of  since there is no convention – use e.g. mean
128.5 (SD 10.35)mmHg
20
Presentation of the analysis results
o
o
o
o
o
formal analysis should be chosen to most efficiently answer
the study hypotheses
actual p-values should be quoted e.g. p=0.21, p=0.003,
p<0.001
confidence intervals are preferable to p-values
assumptions must be validated (e.g. normally distributed)
problems arising from multiple testing should be addressed
21
NHS Scotland National HAI Prevalence Survey. Volume 1 of 2. Final
Report
Health Protection Scotland, 2007
http://www.hps.scot.nhs.uk/haiic/publicationsdetail.aspx?id=34832
22
Whenever you have a table with percentages or
means
ALWAYS INCLUDE
The number of observations on which the mean or
percentage is based
Gives you an impression of precision
23
Decrease
Increase
Decrease
Doubled
Over 75s immune
Weekly Influenza Situation Report (Including H1N1v)
Wednesday 28 October 2009
http://www.documents.hps.scot.nhs.uk/respiratory/swineinfluenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
24
Swab Positivity
70
Using graphs without
numbers or precision is
just as bad
60
Percentage
50
40
30
Week 42
20
Week 43
10
0
0-4
5-14
15-44
45-64
65-74
75+
Age
Swab Positivity
70
70
60
60
50
50
40
30
Week 42
20
Week 43
Percentage
Percentage
Swab Positivity
40
30
Week 42
20
Week 43
10
10
0
0
0-4
5-14
15-44
45-64
Age
65-74
75+
0-4
5-14
15-44
45-64
65-74
75+
Age
25
Weekly Influenza Situation Report (Including H1N1v)
Wednesday 28 October 2009
http://www.documents.hps.scot.nhs.uk/respiratory/swineinfluenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
26
Weekly Influenza Situation Report (Including H1N1v)
Wednesday 28 October 2009
http://www.documents.hps.scot.nhs.uk/respiratory/swineinfluenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
27
Most hospitalisations
among 15-24
Relatively flat
distribution up to 54
Weekly Influenza Situation Report (Including H1N1v)
Wednesday 28 October 2009
http://www.documents.hps.scot.nhs.uk/respiratory/swineinfluenza/situation-reports/weekly-influenza-sitrep-2009-10-29.pdf
28
29
40
20
Easily See
0
Frequency
60
Males
0
20
40
60
80
Peak at 0-4 in both males
and female
Age
More boys 0-4 in hospital
than girls 0-4
20
40
Peak 20-24 year old
women
0
Frequency
60
Females
0
20
40
60
80
Age
30
Report on Review of Clostridium difficile Associated Disease Cases and Mortality in all Acute Hospitals in
Scotland from December 2007 ─ May 2008
Health Protection Scotland
http://www.documents.hps.scot.nhs.uk/hai/sshaip/publications/cdad/cdad-review-2008-07.pdf
31
100
Total Growth During Study
Growth
50
Change Over
10
Ward 4 Clean
W6 No Clean
W4 No Clean
W6 Clean
0
10
20
30
40
50
Week
Measuring the effect of enhanced cleaning in a UK hospital: a
prospective cross-over study
Stephanie J Dancer, Liza F White, Jim Lamb, E Kirsty Girvan and Chris Robertson
BMC Medicine 2009, 7:28 doi:10.1186/1741-7015-7-28
32
Summary
o
o
l
l
Statistical presentation of results must provide scientific
evidence to back up claims made in a report
conclusions must be reliable and based upon data
key aspect of statistics is design, analysis and presentation
of results in the presence of VARIABILITY.
honest presentation requires the inclusion of information to
assess precision (variability) of results
n
n
n
sample sizes,
standard deviations,
confidence intervals
33
Recommended Text Books
o An introduction to medical statistics – J. Martin Bland
o Practical statistics for medical research – Douglas G.
Altman
o Essential medical statistics – Betty Kirkwood and Jonathan
Sterne
o BMJ series of statistical methods (Martin Bland/Douglas
Altman)
o http://openwetware.org/wiki/BMJ_Statistics_Notes_series
o http://www-users.york.ac.uk/~mb55/pubs/pbstnote.htm
34